The utilisation of Plug-and-Play (PnP) priors in inverse problems has become increasingly prominent in recent years. This preference is based on the mathematical equivalence between the general proximal operator and the regularised denoiser, facilitating the adaptation of various off-the-shelf denoiser priors to a wide range of inverse problems. However, existing PnP models predominantly rely on pre-trained denoisers using large datasets. In this work, we introduce Single-Shot PnP methods (SS-PnP), shifting the focus to solving inverse problems with minimal data. First, we integrate Single-Shot proximal denoisers into iterative methods, enabling training with single instances. Second, we propose implicit neural priors based on a novel function that preserves relevant frequencies to capture fine details while avoiding the issue of vanishing gradients. We demonstrate, through extensive numerical and visual experiments, that our method leads to better approximations.

翻译：近年来，即插即用（PnP）先验在逆问题中的应用日益突出。这种偏好基于广义邻近算子与正则化去噪器之间的数学等价性，使得多种现成的去噪器先验能够适配广泛的逆问题。然而，现有的PnP模型主要依赖于使用大型数据集预训练的去噪器。本工作中，我们提出了单次即插即用方法（SS-PnP），将研究重点转向使用极少数据求解逆问题。首先，我们将单次邻近去噪器集成到迭代方法中，实现单样本训练。其次，我们提出基于新型函数的隐式神经先验，该函数能保留相关频率以捕捉细节特征，同时避免梯度消失问题。通过大量的数值与可视化实验，我们证明所提方法能够获得更优的近似解。